Analogical Minds

Abstracts: https://sites.google.com/site/analogylist/analogical-minds-seminar/analogy-and-law-symposium

Understanding what makes human unique is a fundamental research drive for comparative psychologists. Cognitive abilities such as theory of mind, cooperation or mental time travel have been considered uniquely human. Despite empirical evidence showing that animals other than humans are able (to some extent) of these cognitive achievements, findings are still heavily contested. In this context, being able to abstract relations of similarity has also been considered one of the hallmarks of human cognition. While previous research has shown that other animals (e.g., primates) can attend to relational similarity, less is known about what invertebrates can do. In this talk, I will present a series of spatial matching tasks that previously were used with children and great apes and that I adapted for use with wild-caught bumblebees. The findings from these studies suggest striking similarities between vertebrates and invertebrates in their abilities to attend to relational similarity.

Humans are natural teachers; learning through instruction is one of the most fundamental ways that we learn. Interactive Task Learning (ITL) is an emerging research agenda that studies the design of complex intelligent robots that can acquire new knowledge through natural human teacher-robot learner interactions. ITL methods are particularly useful for designing intelligent robots whose behavior can be adapted by humans collaborating with them. In this talk, I will summarize our recent findings on the structure that human instruction naturally has and motivate an intelligent system design that can exploit their structure. The system – AILEEN – is being developed using the common model of cognition. Architectures that implement the Common Model of Cognition - Soar, ACT-R, and Sigma - have a prominent place in research on cognitive modeling as well as on designing complex intelligent agents. However, they miss a critical piece of intelligent behavior – analogical reasoning and generalization. I will introduce a new memory – concept memory – that integrates with a common model of cognition architecture and supports ITL.

Explicit similarity judgments tend to emphasize relational information more than do difference judgments. In this talk, I propose and test the hypothesis that this asymmetry arises because human reasoners represent the relation different as the negation of the relation same (i.e., as not-same). This proposal implies that processing difference is more cognitively demanding than processing similarity. Both for verbal comparisons between word pairs, and for visual comparisons between sets of geometric shapes, participants completed a triad task in which they selected which of two options was either more similar to or more different from a standard. On unambiguous trials, one option was unambiguously more similar to the standard, either by virtue of featural similarity or by virtue of relational similarity. On ambiguous trials, one option was more featurally similar (but less relationally similar) to the standard, whereas the other was more relationally similar (but less featurally similar). Given the higher cognitive complexity of assessing relational similarity, we predicted that detecting relational difference would be particularly demanding. We found that participants (1) had more difficulty accurately detecting relational difference than they did relational similarity on unambiguous trials, and (2) tended to emphasize relational information more when judging similarity than when judging difference on ambiguous trials. The latter finding was captured by a computational model of comparison that weights relational information more heavily for similarity than for difference judgments. These results provide convergent evidence for a representational asymmetry between the relations same and different.

Analogical reasoning is a common reasoning tool for learning and problem-solving. Existing research has extensively studied children’s reasoning when comparing, or choosing from ready-made analogies. Relatively less is known about how children come up with analogies in authentic learning environments. Design education provides a suitable context to investigate how children generate analogies for creative learning purposes. Meanwhile, the frequent use of visual analogies in design provides an additional opportunity to understand the role of spatial reasoning in design-by-analogy. Spatial reasoning is one of the most studied human cognitive factors and is critical to the learning of science, technology, engineering, arts, and mathematics (STEAM). There is growing interest in exploring the interplay between analogical reasoning and spatial reasoning. In this talk, I will share qualitative findings from a case study, where a class of 11-to-12-year-olds in the Netherlands participated in a biomimicry design project. These findings illustrate (1) practical ways to support children’s analogical reasoning in the ideation process and (2) the potential role of spatial reasoning as seen in children mapping form-function relationships in nature analogically and adaptively to those in human designs.

Metaphor is a pervasive phenomenon in language and cognition. To date, the vast majority of psycholinguistic research on metaphor has focused on noun-noun metaphors of the form An X is a Y (e.g., My job is a jail). Yet there is evidence that verb metaphor (e.g., I sailed through my exams) is more common. Despite this, comparatively little work has examined how verb metaphors are processed. In this talk, I will propose a novel account for verb metaphor comprehension: verb metaphors are understood in the same way that analogies are—as comparisons processed via structure-mapping. I will discuss the predictions that arise from applying the analogical framework to verb metaphor and present a series of experiments showing that verb metaphoric extension is consistent with those predictions.

In cognitive development, learning more than the input provides is a central challenge. This challenge is especially evident in learning the meaning of numbers. Integers – and the quantities they denote – are potentially infinite, as are the fractional values between every integer. Yet children’s experiences of numbers are necessarily finite. Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input. However, retrieving proper analogy requires cognitive supports. In this talk, I seek to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning. To examine these hypotheses, I will present a series of educational intervention studies with third-to-fifth graders. Results showed that a short, unsupervised intervention of spatial alignment between integers and fractions on number lines produced broad and durable gains in fractional magnitudes. Additionally, training on conceptual knowledge of fractions – that fractions denote magnitude and can be placed on number lines – facilitates explicit analogical reasoning. Together, these studies indicate that analogies can play an important role in rational number learning with the help of number lines as schemas. These studies shed light on helpful practices in STEM education curricula and instructions.

In this presentation, we will discuss adaptations of historical examples of mathematical research to bring out some of the intuitive judgments that accompany the working practice of mathematicians when reasoning by analogy. The main epistemological claim that we will aim to illustrate is that a central part of mathematical training consists in developing a quasi-perceptual capacity to distinguish superficial from deep analogies. We think of this capacity as an instance of Hadamard’s (1954) discriminating faculty of the mathematical mind, whereby one is led to distinguish between mere “hookings” (77) and “relay-results” (80): on the one hand, suggestions or ‘hints’, useful to raise questions but not to back up conjectures; on the other, more significant discoveries, which can be used as an evidentiary source in further mathematical inquiry. In the second part of the presentation, we will present some recent applications of this epistemological framework to mathematics education projects for middle and high schools in Italy.

In this talk, I’ll consider how new ideas emerge from old ones via the process of conceptual blending. I’ll start by considering analogical reasoning in problem solving and the role conceptual blending plays in these problem-solving contexts. Then I’ll consider blending in multi-modal contexts, including timelines, memes (viz. image macros), and, if time allows, zoom meetings. I suggest mappings analogy researchers have traditionally considered superficial are often important for the development of novel abstractions. Likewise, the analogue portion of multimodal blends anchors their generative capacity. Overall, these observations underscore the extent to which meaning is a socially distributed process whose intermediate products are stored in cognitive artifacts such as text and digital images.

Learning verbs is difficult and critical to learning one's native language. Children appear to benefit from seeing multiple events and comparing them to each other, and structural alignment theory provides a good theoretical framework to guide research into how preschool children may be comparing events as they learn new verbs. The talk will include 6 studies of early verb learning that make use of eye-tracking procedures as well as other behavioral (pointing) procedures, and that test key predictions from SA theory including the prediction that seeing similar examples before more varied examples helps observers learn how to compare (progressive alignment) and the prediction that when events have very low alignability with other events, that is one cue that the events should be ignored. Whether or how statistical learning may also be at work will be considered.

Vector-space models are used frequently to compare similarity and dimensionality among entity concepts. What happens when we apply these models to relational concepts? What is the evidence that such models do apply to relational concepts? If we use such a model, then one implication is that maximizing surface feature variation should improve relational concept learning. For example, in STEM instruction, the effectiveness of teaching by analogy is often limited by students’ focus on superficial features of the source and target exemplars. However, in contrast to the prediction of the vector-space computational model, the strategy of progressive alignment (moving from perceptually similar to different targets) has been suggested to address this issue (Gentner & Hoyos, 2017), and human behavioral evidence has shown benefits from progressive alignment. Here I will present some preliminary data that supports the computational approach. Participants were explicitly instructed to match stimuli based on relations while perceptual similarity of stimuli varied parametrically. We found that lower perceptual similarity reduced accurate relational matching. This finding demonstrates that perceptual similarity may interfere with relational judgements, but also hints at why progressive alignment maybe effective. These are preliminary, exploratory data and I to hope receive feedback on the framework and to start a discussion in a group on the utility of vector-space models for relational concepts in general.

Following the seminal structure mapping theory by Dedre Gentner, the process of mapping the corresponding structures of relations defining two analogs has been understood as a key component of analogy making. However, not without a merit, in recent years some semantic, pragmatic, and perceptual aspects of analogy mapping attracted primary attention of analogy researchers. For almost a decade, our team have been re-focusing on relational structure mapping, investigating its potential mechanisms across various analogy tasks, both abstract (semantically-lean) and more concrete (semantically-rich), using diverse methods (behavioral, correlational, eye-tracking, EEG). I will present the overview of our main findings. They suggest that structure mapping (1) consists of an incremental construction of the ultimate mental representation, (2) which strongly depends on working memory resources and reasoning ability, (3) even if as little as a single trivial relation needs to be represented mentally. The effective mapping (4) is related to the slowest brain rhythm – the delta band (around 2-3 Hz) – suggesting its highly integrative nature. Finally, we have developed a new task – Graph Mapping – which involves pure mapping of two explicit relational structures. This task allows for precise investigation and manipulation of the mapping process in experiments, as well as is one of the best proxies of individual differences in reasoning ability. Structure mapping is as crucial to analogy as Gentner advocated, and perhaps it is crucial to cognition in general.

Can nonhuman animals perceive the relation-between-relations? This intriguing question has been studied over the last 40 years; nonetheless, the extent to which nonhuman species can do so remains controversial. Here, I review empirical evidence suggesting that pigeons, parrots, crows, and baboons join humans in reliably acquiring and transferring relational matching-to-sample (RMTS). Many theorists consider that RMTS captures the essence of analogy, because basic to analogy is appreciating the ‘relation between relations.’ Factors affecting RMTS performance include: prior training experience, the entropy of the sample stimulus, and whether the items that serve as sample stimuli can also serve as choice stimuli.

Dominant theories of analogical thinking postulate that making an analogy consists in discovering that two superficially different situations share isomorphic systems of similar relations. According to this perspective, the comparison between the two situations may eventually lead to the construction of a schema, which retains the structural aspects they share and deletes their specific contents. We have developed a new approach to analogical thinking, whose purpose is to explain a particular type of analogies: those in which the analogs are exemplars of a schema-governed category (e.g., two instances of robbery). As compared to standard analogies, these comparisons are noteworthy in that a well-established schema (the schema-governed category) mediates each one of the subprocesses involved in analogical thinking. We argue that the category assignment approach is able to provide a better account of how the analogical subprocesses of retrieval, mapping, re-representation, evaluation and inference generation are carried out during the processing of this specific kind of analogies. The arguments presented are accompanied by brief descriptions of some of the studies that provided support for this approach.

What do people do when they comprehend language in discourse? According to many psychologists, they build and maintain cognitive representations of utterances in four complementary mental models for discourse that interact with each other: the surface text, the text base, the situation model, and the context model. When people encounter metaphors in these utterances, they need to incorporate them into each of these mental representations for the discourse. Since influential metaphor theories define metaphor as a form of (figurative) analogy, involving cross-domain mapping of a smaller or greater extent, the general expectation has been that metaphor comprehension is also based on analogizing. This expectation, however, has been partly borne out by the data, but not completely. There is no one-to-one relationship between metaphor as (conceptual) structure (analogy) and metaphor as (psychological) process (analogizing). According to Deliberate Metaphor Theory (DMT), only some metaphors are handled by analogy. Instead, most metaphors are presumably handled by lexical disambiguation. This is a hypothesis that brings together most metaphor research in a provocatively new way: it means that most metaphors are not processed metaphorically, which produces a paradox of metaphor. In this talk I will sketch out how this paradox arises and how it can be resolved by a new version of DMT, which I have described in my forthcoming book Slowing metaphor down: Updating Deliberate Metaphor Theory (currently under review). In this theory, the distinction between, but also the relation between, analogy in metaphorical structure versus analogy in metaphorical process is of central importance.

Analogical reasoning –learning about new things by relating it to previous knowledge– lies at the heart of human intelligence and creativity and forms the core of educational practice. Children start creating and using analogies early on, making incredible progress moving from associative processes to successful analogical reasoning. For example, if we ask a four-year-old “Horse belongs to stable like chicken belongs to …?” they may use association and reply “egg”, whereas older children will likely give the intended relational response “chicken coop” (or other term to refer to a chicken’s home). Interestingly, despite state-of-the-art AI-language models having superhuman encyclopedic knowledge and superior memory and computational power, our pilot studies show that these large language models often make mistakes providing associative rather than relational responses to verbal analogies. For example, when we asked four- to eight-year-olds to solve the analogy “body is to feet as tree is to …?” they responded “roots” without hesitation, but large language models tend to provide more associative responses such as “leaves”. In this study we examine the similarities and differences between children's and six large language models' (Dutch/multilingual models: RobBERT, BERT-je, M-BERT, GPT-2, M-GPT, Word2Vec and Fasttext) responses to verbal analogies extracted from an online adaptive learning environment, where >14,000 7-12 year-olds from the Netherlands solved 20 or more items from a database of 900 Dutch language verbal analogies.

Analogies between old and new concepts are common during classroom instruction. While previous studies of transfer focus on how features of initial learning guide later transfer to new problem solving, less is known about how to best support analogical transfer from previous learning while children are engaged in new learning episodes. Such research may have important implications for teaching and learning in mathematics, which often includes analogies between old and new information. Some existing research promotes supporting learners' explicit connections across old and new information within an analogy. In this talk, I will present evidence that instructors can invite implicit analogical reasoning through warm-up activities designed to activate relevant prior knowledge. Warm-up activities "close the transfer space" between old and new learning without additional direct instruction.

Relational thinking involves comparing abstract relationships between mental representations that vary in complexity; however, this complexity is rarely made explicit during everyday comparisons. This study explored how people naturally navigate relational complexity and interference using a novel relational match-to-sample (RMTS) task with both minimal and relationally directed instruction to observe changes in performance across three levels of relational complexity: perceptual, analogy, and system mappings. Individual working memory and relational abilities were examined to understand RMTS performance and susceptibility to interfering relational structures. Trials were presented without practice across four blocks and participants received feedback after each attempt to guide learning. Experiment 1 instructed participants to select the target that best matched the sample, while Experiment 2 additionally directed participants’ attention to same and different relations. Participants in Experiment 2 demonstrated improved performance when solving analogical mappings, suggesting that directing attention to relational characteristics affected behavior. Higher performing participants—those above chance performance on the final block of system mappings—solved more analogical RMTS problems and had greater visuospatial working memory, abstraction, verbal analogy, and scene analogy scores compared to lower performers. Lower performers were less dynamic in their performance across blocks and demonstrated negative relationships between analogy and system mapping accuracy, suggesting increased interference between these relational structures. Participant performance on RMTS problems did not change monotonically with relational complexity, suggesting that increases in relational complexity places nonlinear demands on working memory. We argue that competing relational information causes additional interference, especially in individuals with lower executive function abilities.

Humans perceive the world in terms of objects and relations between them. In fact, for any given pair of objects, there is a myriad of relations that apply to them. How does the cognitive system learn which relations are useful to characterize the task at hand? And how can it use these representations to build a relational policy to interact effectively with the environment? In this paper we propose that this problem can be understood through the lens of a sub-field of symbolic machine learning called relational reinforcement learning (RRL). To demonstrate the potential of our approach, we build a simple model of relational policy learning based on a function approximator developed in RRL. We trained and tested our model in three Atari games that required to consider an increasingly number of potential relations: Breakout, Pong and Demon Attack. In each game, our model was able to select adequate relational representations and build a relational policy incrementally. We discuss the relationship between our model with models of relational and analogical reasoning, as well as its limitations and future directions of research.